--- a/src/HOL/arith_data.ML Fri Dec 05 11:26:07 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,157 +0,0 @@
-(* Title: HOL/arith_data.ML
- ID: $Id$
- Author: Markus Wenzel, Stefan Berghofer, and Tobias Nipkow
-
-Basic arithmetic proof tools.
-*)
-
-signature ARITH_DATA =
-sig
- val prove_conv: tactic -> (MetaSimplifier.simpset -> tactic)
- -> MetaSimplifier.simpset -> term * term -> thm
- val simp_all_tac: thm list -> MetaSimplifier.simpset -> tactic
-
- val mk_sum: term list -> term
- val mk_norm_sum: term list -> term
- val dest_sum: term -> term list
-
- val nat_cancel_sums_add: simproc list
- val nat_cancel_sums: simproc list
- val setup: Context.generic -> Context.generic
-end;
-
-structure ArithData: ARITH_DATA =
-struct
-
-(** generic proof tools **)
-
-(* prove conversions *)
-
-fun prove_conv expand_tac norm_tac ss tu = (* FIXME avoid standard *)
- mk_meta_eq (standard (Goal.prove (Simplifier.the_context ss) [] []
- (HOLogic.mk_Trueprop (HOLogic.mk_eq tu))
- (K (EVERY [expand_tac, norm_tac ss]))));
-
-(* rewriting *)
-
-fun simp_all_tac rules =
- let val ss0 = HOL_ss addsimps rules
- in fn ss => ALLGOALS (simp_tac (Simplifier.inherit_context ss ss0)) end;
-
-
-(** abstract syntax of structure nat: 0, Suc, + **)
-
-local
-
-val mk_plus = HOLogic.mk_binop @{const_name HOL.plus};
-val dest_plus = HOLogic.dest_bin @{const_name HOL.plus} HOLogic.natT;
-
-in
-
-fun mk_sum [] = HOLogic.zero
- | mk_sum [t] = t
- | mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
-
-(*normal form of sums: Suc (... (Suc (a + (b + ...))))*)
-fun mk_norm_sum ts =
- let val (ones, sums) = List.partition (equal HOLogic.Suc_zero) ts in
- funpow (length ones) HOLogic.mk_Suc (mk_sum sums)
- end;
-
-
-fun dest_sum tm =
- if HOLogic.is_zero tm then []
- else
- (case try HOLogic.dest_Suc tm of
- SOME t => HOLogic.Suc_zero :: dest_sum t
- | NONE =>
- (case try dest_plus tm of
- SOME (t, u) => dest_sum t @ dest_sum u
- | NONE => [tm]));
-
-end;
-
-
-(** cancel common summands **)
-
-structure Sum =
-struct
- val mk_sum = mk_norm_sum;
- val dest_sum = dest_sum;
- val prove_conv = prove_conv;
- val norm_tac1 = simp_all_tac [@{thm "add_Suc"}, @{thm "add_Suc_right"},
- @{thm "add_0"}, @{thm "add_0_right"}];
- val norm_tac2 = simp_all_tac @{thms add_ac};
- fun norm_tac ss = norm_tac1 ss THEN norm_tac2 ss;
-end;
-
-fun gen_uncancel_tac rule ct =
- rtac (instantiate' [] [NONE, SOME ct] (rule RS @{thm subst_equals})) 1;
-
-
-(* nat eq *)
-
-structure EqCancelSums = CancelSumsFun
-(struct
- open Sum;
- val mk_bal = HOLogic.mk_eq;
- val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT;
- val uncancel_tac = gen_uncancel_tac @{thm "nat_add_left_cancel"};
-end);
-
-
-(* nat less *)
-
-structure LessCancelSums = CancelSumsFun
-(struct
- open Sum;
- val mk_bal = HOLogic.mk_binrel @{const_name HOL.less};
- val dest_bal = HOLogic.dest_bin @{const_name HOL.less} HOLogic.natT;
- val uncancel_tac = gen_uncancel_tac @{thm "nat_add_left_cancel_less"};
-end);
-
-
-(* nat le *)
-
-structure LeCancelSums = CancelSumsFun
-(struct
- open Sum;
- val mk_bal = HOLogic.mk_binrel @{const_name HOL.less_eq};
- val dest_bal = HOLogic.dest_bin @{const_name HOL.less_eq} HOLogic.natT;
- val uncancel_tac = gen_uncancel_tac @{thm "nat_add_left_cancel_le"};
-end);
-
-
-(* nat diff *)
-
-structure DiffCancelSums = CancelSumsFun
-(struct
- open Sum;
- val mk_bal = HOLogic.mk_binop @{const_name HOL.minus};
- val dest_bal = HOLogic.dest_bin @{const_name HOL.minus} HOLogic.natT;
- val uncancel_tac = gen_uncancel_tac @{thm "diff_cancel"};
-end);
-
-
-(* prepare nat_cancel simprocs *)
-
-val nat_cancel_sums_add =
- [Simplifier.simproc (the_context ()) "nateq_cancel_sums"
- ["(l::nat) + m = n", "(l::nat) = m + n", "Suc m = n", "m = Suc n"]
- (K EqCancelSums.proc),
- Simplifier.simproc (the_context ()) "natless_cancel_sums"
- ["(l::nat) + m < n", "(l::nat) < m + n", "Suc m < n", "m < Suc n"]
- (K LessCancelSums.proc),
- Simplifier.simproc (the_context ()) "natle_cancel_sums"
- ["(l::nat) + m <= n", "(l::nat) <= m + n", "Suc m <= n", "m <= Suc n"]
- (K LeCancelSums.proc)];
-
-val nat_cancel_sums = nat_cancel_sums_add @
- [Simplifier.simproc (the_context ()) "natdiff_cancel_sums"
- ["((l::nat) + m) - n", "(l::nat) - (m + n)", "Suc m - n", "m - Suc n"]
- (K DiffCancelSums.proc)];
-
-val setup =
- Simplifier.map_ss (fn ss => ss addsimprocs nat_cancel_sums);
-
-end;